Problem3:

The curve,

> ;

```                                     2
y = a x  + b x + c```
 passes through the points (x1,y1), (x2,y2), (x3,y3). Show that the coefficients a,b, and c are a solution of the system of linear equations whose augmented matrix is,

> ;

```                            [  2                 ]
[x1     x1    1    y1]
[                    ]
[  2                 ]
[x2     x2    1    y2]
[                    ]
[  2                 ]
[x3     x3    1    y3]```

SOLUTION:

 Each pt. (x,y) on the plane produces the equation of the curve. i.e.,

> Eq := (x,y) -> a*x^2+b*x+c = y;

```                                         2
Eq := (x, y) -> a x  + b x + c = y```
 since the curve must pass through each of the given points we have 3 equations in the unknowns a,b and c given by,

> Eq(x1,y1); Eq(x2,y2); Eq(x3,y3);

```                                 2
a x1  + b x1 + c = y1

2
a x2  + b x2 + c = y2

2
a x3  + b x3 + c = y3```
 hence, the augmented matrix is the one specified in the problem.

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>